An official donation of £500 or more must be given by a "permissible donor", who should either be somebody listed on the UK electoral roll or a business registered at Companies House and operating in the UK.

The Brexit Party has updated its website to say that those making donations or becoming registered supporters must comply with those requirements.

At an event in Glasgow on Monday, Mr Brown said there was no way of telling whether donations to The Brexit Party - which can be made through PayPal - come from British or foreign sources, and therefore the system was being abused.

Other political parties - including the Conservatives and Labour - also use PayPal to collect donations on their websites.

"You can pay to this party in Russian roubles or American dollars," Mr Brown said.

"Democracy is ill served, and trust in democracy will continue to be undermined, if we have no answers as to where the money is coming from," he added.

Labour MP Chris Bryant has also said the system is open to abuse.

Responding to the Mr Brown's comments, Mr Farage said: "Most of our money has been raised by people giving £25 to become registered supporters."

"And over 110,000 of them now have done that. And frankly, this smacks of jealousy because the other parties simply can't do this."

When asked if the party took donations in foreign currency, Mr Farage replied: "Absolutely not, we only take sterling - end of conversation."

Shadow chancellor John McDonnell called for "a full and open and transparent, independent inquiry into the funding of Mr Farage".

Asked if he could confirm whether the party takes cash from foreign citizens, Mr Tice said: "I don't sit in front of the PayPal account all day so I don't know what currencies people are paying in, but, as I understand it, the PayPal takes it in sterling."

The Conservative Party said it required people to give their name and address before contributing £500 or more.

Change UK said: "We identify all donors, including those under the £500 threshold, so that we can conduct a permissibility check should the aggregate of donations per donor exceed the £500 threshold."

In 2013, the Electoral Commission issued guidance to parties that "if a donor makes regular payments for an unspecified donation and towards an unspecified total amount, our view is that these payments should be treated as separate donations."

Analysis: By Jessica Parker, BBC political correspondent

As you might expect, the world of party funding and finance is a complicated one. But an interesting element to pin-point is this issue of smaller donations.

Under UK law a donation to a political party that's under £500 does not have to be reported to the Electoral Commission. In fact, that kind of financial contribution doesn't even count as a donation. So, for example, the usual rules around the money having to come from a UK elector or UK-registered company don't apply.

What wouldn't be allowed are repeated small donations, from the same source, in order to dodge the donation limits.

Significantly, these rules originate from legislation that's nearly 20 years old - the Political Parties, Elections and Referendums Act 2000. Back then, they probably didn't worry about the risk that parties might be able to crowdfund from foreign donors, and one academic's told me that the law is no longer "fit for purpose".

Meanwhile, when it comes to the Electoral Commission's plan to visit The Brexit Party's offices - I understand that officials and the party have been in dialogue for several weeks and that's it's not necessarily unusual for the commission to meet parties to ensure that their systems are up to scratch. However, it appears that the commission hasn't yet visited any others during this particular campaign.

During his speech, Gordon Brown also attacked Mr Farage for receiving £450,000 from Leave campaigner Arron Banks while still a member of the European Parliament.

Mr Brown said The Brexit Party leader should have declared the payments he was receiving "to avoid a conflict of interest".

Asked about it following an investigation by Channel 4 News, Mr Farage said he did not declare it to the European Parliament because he was about to leave politics and had been seeking a new life in the US.

Lib Dem MEP Catherine Bearder has written to the President of the European Parliament Antonio Tajani calling for an investigation into the matter. Green MEP Molly Scott Cato said she had also referred Mr Farage to the European Anti-Fraud Office.

Meanwhile, a man has been charged with assaulting Nigel Farage by throwing a milkshake at him.

The Brexit Party leader had given a speech in Newcastle on Monday ahead of the European elections when the incident happened.